/*********************************************************************************************** # statusexchangemodels.do # Aaron Gullickson # UO Sociology # 5/4/2015 # # The purpose of this program is to show the basic code needed to produce the status # exchange models used in Gullickson and Torche (2014) and Gullickson (2006). The # code will produce market exchange and dyadic exchange terms for the data. It will also # show how to incorporate geometric means terms to estimate the baseline expectation about # assortative mating for interracial couples. Finally, it will show why Rosenfeld's models # of status exchange from his AJS article are overfit and thus bad models. # PLEASE NOTE: You need to install the desmat library in order to run this do file ***********************************************************************************************/ /*********************************************************************************************** # THE DATA # The data used here is a 2x2x4x4 table (flattened) of husband's race by wife's race by # husband's education by wife's education. Race is white (1) and black (2). Education is # less than high school (1), high school (2), some college (3), and college+ (4). The data # come from the US Census 1990, but PLEASE NOTE that I found this data lying around in # and cannot vouch for its completeness or representativeness. It is being used for # demonstrative purposes and inferences and conclusions should not be drawn from it ***********************************************************************************************/ insheet using usmardata1990.csv *do some renaming because stata stupidly changes the case on my variable names unlike R rename hr HR rename wr WR rename he HE rename we WE rename freq Freq /*********************************************************************************************** # DYADIC EXCHANGE TERMS # I simply code a set of dummy variables for cases of non-homogamy among interracial couples. # This is coded separately by the gender combination of the couple (BM/WF vs. WM/BF) and whether # it implies upward or downward marriage for the black partner (not the woman). ***********************************************************************************************/ generate SEBMWFUp = HE>WE & HR==2 & WR==1 generate SEBMWFDown = HEHE & HR==1 & WR==2 generate SEWMBFDown = WEWE & HR==2 & WR==1 replace SEBMWF = -1 if HEWE & HR==1 & WR==2 *Here is the most parsimonious term which assumes both directional symmetry *and identical effects for BM/WF and WM/BF couples. generate SE = SEBMWF+SEWMBF /*********************************************************************************************** # MARKET EXCHANGE TERMS # These terms are synonomous with the educational boundary terms in Gullickson (2006) which are # themselves very similar to the terms used by FU (2001). As I will show below these terms are # actually identical to fitting the three way HR*WR*HE and HR*WR*HE (and lower ordered HR*WE # and WR*HE) tables, but this particular coding scheme makes the results more interpretable. # I use "stairstep" coding here, such that each level of education gets the effect for that level # PLUS the effect for lower levels. Using this technique means that each coefficient measures the # difference between adjacent levels of education (e.g. college vs. some college) rather than # between that level and a fixed reference (e.g. college vs. less than high school). I also # included a commented out more traditional dummy formulation for users that prefer that style. # # Each term here can be thought of as the increase in the likelihood of interracial marriage # when education increases by one level for each race-gender type (i.e. black men, black women, # white men, white women). ***********************************************************************************************/ generate EBBM1 = HE>1 & HR==2 & WR==1 generate EBBM2 = HE>2 & HR==2 & WR==1 generate EBBM3 = HE>3 & HR==2 & WR==1 generate EBWF1 = WE>1 & HR==2 & WR==1 generate EBWF2 = WE>2 & HR==2 & WR==1 generate EBWF3 = WE>3 & HR==2 & WR==1 generate EBWM1 = HE>1 & HR==1 & WR==2 generate EBWM2 = HE>2 & HR==1 & WR==2 generate EBWM3 = HE>3 & HR==1 & WR==2 generate EBBF1 = WE>1 & HR==1 & WR==2 generate EBBF2 = WE>2 & HR==1 & WR==2 generate EBBF3 = WE>3 & HR==1 & WR==2 *alternate coding by dummy approach (commented out by default) /* generate EBBM1 = HE==2 & HR==2 & WR==1 generate EBBM2 = HE==3 & HR==2 & WR==1 generate EBBM3 = HE==4 & HR==2 & WR==1 generate EBWF1 = WE==2 & HR==2 & WR==1 generate EBWF2 = WE==3 & HR==2 & WR==1 generate EBWF3 = WE==4 & HR==2 & WR==1 generate EBWM1 = HE==2 & HR==1 & WR==2 generate EBWM2 = HE==3 & HR==1 & WR==2 generate EBWM3 = HE==4 & HR==1 & WR==2 generate EBBF1 = WE==2 & HR==1 & WR==2 generate EBBF2 = WE==3 & HR==1 & WR==2 generate EBBF3 = WE==4 & HR==1 & WR==2 */ /*********************************************************************************************** # GEOMETRIC MEAN OF HE*WE # One of Rosenfeld's criticisms of prior research is that it did not correctly account for lower-order # interaction terms when estimating the status exchange parameter. He argues that the status exchange term #is a parameterized coding of the HE*WE*HR*WR table and thus it is necessary to fit all the three-way and # two-way interactions. This includes HR*WR*HE, HR*WR*WE, HR*HE*WE, WR*HE*WE, HR*WE, and WR*HE. As the # appendix to Gullickson and Torche (2014) makes clear, Rosenfeld is wrong about the nature of the dyadic # status exchange term. It is actually a parameterized coding of the HE*WE*HR and HE*WE*WR tables. As a result, # when Rosenfeld includes these terms, his models are overfit, as I will show below. The HR*WR*HE and HR*WR*WE # tables are also identical to the market exchange terms coded here which can be thought of as an alternate way # of measuring exchange rather than a nuisance control term. For more details, see Gullickson and Torche (2014) # and the appendix, Gullickson and Fu (2010), and Kalmijn (2010). # # Despite this inherent problems. Rosenfeld's criticism does reveal one potential shortcoming of the way these # models are estimated. When estimating how different the educational assorative mating is for interracial couples # (i.e. whether status exchange is occurring), interracial couples are implicitly being compared to the pooled # tabled for white and black endogamous couples. But if white and black couples themselves differ in their patterns # of ed assortative mating, then the results may be misleading. Probably the best way to handle this is that # suggested by Kalmijn (1993) in which the baseline assumption about the educational assortative mating of # black/white couples is taken as the geometric mean of the educational asortative mating (HE*WE) of white and # black endogamous couples. Gullickson and Torche (2014) discusses this in more detail (particularly the # appendix). Ultimately we found the results to be similar using the geometric mean (and a few other # specifications) as the more naive approach, but it is worth testing on a data set specific basis. # # The way of coding this geometric mean is a bit tedious. I fit dummies for each of the nine terms in the HE*WE # table separately for white endogmous and black endogamous couples and then allow interracial couples to be a # 0.5 on each dummy. ***********************************************************************************************/ generate WWHEWE1 = (HR==1 & WR==1 & HE==2 & WE==2) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==2 & WE==2) generate WWHEWE2 = (HR==1 & WR==1 & HE==2 & WE==3) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==2 & WE==3) generate WWHEWE3 = (HR==1 & WR==1 & HE==2 & WE==4) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==2 & WE==4) generate WWHEWE4 = (HR==1 & WR==1 & HE==3 & WE==2) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==3 & WE==2) generate WWHEWE5 = (HR==1 & WR==1 & HE==3 & WE==3) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==3 & WE==3) generate WWHEWE6 = (HR==1 & WR==1 & HE==3 & WE==4) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==3 & WE==4) generate WWHEWE7 = (HR==1 & WR==1 & HE==4 & WE==2) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==4 & WE==2) generate WWHEWE8 = (HR==1 & WR==1 & HE==4 & WE==3) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==4 & WE==3) generate WWHEWE9 = (HR==1 & WR==1 & HE==4 & WE==4) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==4 & WE==4) generate BBHEWE1 = (HR==2 & WR==2 & HE==2 & WE==2) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==2 & WE==2) generate BBHEWE2 = (HR==2 & WR==2 & HE==2 & WE==3) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==2 & WE==3) generate BBHEWE3 = (HR==2 & WR==2 & HE==2 & WE==4) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==2 & WE==4) generate BBHEWE4 = (HR==2 & WR==2 & HE==3 & WE==2) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==3 & WE==2) generate BBHEWE5 = (HR==2 & WR==2 & HE==3 & WE==3) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==3 & WE==3) generate BBHEWE6 = (HR==2 & WR==2 & HE==3 & WE==4) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==3 & WE==4) generate BBHEWE7 = (HR==2 & WR==2 & HE==4 & WE==2) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==4 & WE==2) generate BBHEWE8 = (HR==2 & WR==2 & HE==4 & WE==3) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==4 & WE==3) generate BBHEWE9 = (HR==2 & WR==2 & HE==4 & WE==4) + 0.5 * (((HR==1 & WR==2) | (HR==2 & WR==1)) & HE==4 & WE==4) /*********************************************************************************************** # THE MODELS # I first run a baseline model which just fits a general term for racial and educational # homogamy (HR*WR and HE*WE) as well as account for the differential distribution of education by # race (HE*HR and WE*WR). This model also fits the four marginal terms themselves, of course. # Then I fit separate dyadic and market exchange models, plus one that combines them both # together. I also run a model with just the straight three way interactions of HR*WR*HE and # HR*WR*WE (model.compare) to show that this model is identical to the market exchange model. ***********************************************************************************************/ *baseline model desmat: glm Freq HR*WR HE*HR WE*WR HE*WE, family(poisson) link(log) *dyadic - full symmetry in terms of up/down and couple type desmat: glm Freq HR*WR HE*HR WE*WR HE*WE @SE, family(poisson) link(log) *dyadic - relax symmetry on couple type but not up/down desmat: glm Freq HR*WR HE*HR WE*WR HE*WE @SEBMWF @SEWMBF, family(poisson) link(log) *dyadic - full model allowing different up/down and couple type desmat: glm Freq HR*WR HE*HR WE*WR HE*WE @SEBMWFUp @SEBMWFDown @SEWMBFUp @SEWMBFDown, family(poisson) link(log) *market model desmat: glm Freq HR*WR HE*HR WE*WR HE*WE @EBBM1 @EBBM2 @EBBM3 @EBWF1 @EBWF2 @EBWF3 /// @EBWM1 @EBWM2 @EBWM3 @EBBF1 @EBBF2 @EBBF3, family(poisson) link(log) *this model just fits the three way interaction terms for HR*WR*HE and HR*WR*HE to show that it fits *identically to the market model. In other words, they are just different parameterizations of the same model. desmat: glm Freq HR*WR HE*HR WE*WR HE*WE HR*WR*HE HR*WR*WE, family(poisson) link(log) *both dyadic and market desmat: glm Freq HR*WR HE*HR WE*WR HE*WE @SEBMWFUp @SEBMWFDown @SEWMBFUp @SEWMBFDown /// @EBBM1 @EBBM2 @EBBM3 @EBWF1 @EBWF2 @EBWF3 @EBWM1 @EBWM2 @EBWM3 @EBBF1 @EBBF2 @EBBF3, family(poisson) link(log) /*********************************************************************************************** # ROSENFELD MODELS # I follow rosenfeld's protocol of adding in all of the missing two and three # way tables and show that his method leads to collinearity such that terms are dropped from the # model. This happens because of collinearity between the HE*WE*HR and HE*WE*WR terms and the # dyadic exchange term. ***********************************************************************************************/ * NOTE: the collinearity is apparently not reported very well, but you can see it in that the HE*WE*WR * term has eight terms instead of the expected nine terms and the overall DF for the model is 9, rather than 8 * (the 9 DF remaining in the four way interaction term, minus the one used for the SE term). The R version of * this code does report the collinearity more clearly. desmat: glm Freq HR*WR HE*HR WE*WR HE*WE HR*WR*HE HR*WR*WE HE*WE*HR HE*WE*WR @SE, family(poisson) link(log) *the same holds for the other dyadic models but I don't show them for brevity *now show that dropping out HE*WE*HR and HE*WE*WR resolves the problem. The resulting model is equivalent * to a model with both a dyadic and market exchange term desmat: glm Freq HR*WR HE*HR WE*WR HE*WE HR*WR*HE HR*WR*WE @SE, family(poisson) link(log) desmat: glm Freq HR*WR HE*HR WE*WR HE*WE @SE @EBBM1 @EBBM2 @EBBM3 @EBWF1 @EBWF2 @EBWF3 @EBWM1 @EBWM2 @EBWM3 @EBBF1 @EBBF2 @EBBF3, /// family(poisson) link(log) /*********************************************************************************************** # GEOMETRIC MEAN MODELS # Here I just rerun the dyadic and market exchange models with the geometric mean baseline rather # than the pooled HE*WE baseline. The results are fairly consistent with what we had before for BM/WF # couples, but not WM/BF couples. ***********************************************************************************************/ *baseline geo modelt desmat: glm Freq HR*WR HE*HR WE*WR @WWHEWE1 @WWHEWE2 @WWHEWE3 @WWHEWE4 @WWHEWE5 @WWHEWE6 @WWHEWE7 @WWHEWE8 @WWHEWE9 /// @BBHEWE1 @BBHEWE2 @BBHEWE3 @BBHEWE4 @BBHEWE5 @BBHEWE6 @BBHEWE7 @BBHEWE8 @BBHEWE9, family(poisson) link(log) *dyadic exchange, full symmetry desmat: glm Freq HR*WR HE*HR WE*WR @SE @WWHEWE1 @WWHEWE2 @WWHEWE3 @WWHEWE4 @WWHEWE5 @WWHEWE6 @WWHEWE7 @WWHEWE8 @WWHEWE9 /// @BBHEWE1 @BBHEWE2 @BBHEWE3 @BBHEWE4 @BBHEWE5 @BBHEWE6 @BBHEWE7 @BBHEWE8 @BBHEWE9, family(poisson) link(log) *dyadic exchange, partial symmetry desmat: glm Freq HR*WR HE*HR WE*WR @SEBMWF @SEWMBF @WWHEWE1 @WWHEWE2 @WWHEWE3 @WWHEWE4 @WWHEWE5 @WWHEWE6 @WWHEWE7 @WWHEWE8 @WWHEWE9 /// @BBHEWE1 @BBHEWE2 @BBHEWE3 @BBHEWE4 @BBHEWE5 @BBHEWE6 @BBHEWE7 @BBHEWE8 @BBHEWE9, family(poisson) link(log) *dyadic exchange, full desmat: glm Freq HR*WR HE*HR WE*WR @SEBMWFUp @SEBMWFDown @SEWMBFUp @SEWMBFDown /// @WWHEWE1 @WWHEWE2 @WWHEWE3 @WWHEWE4 @WWHEWE5 @WWHEWE6 @WWHEWE7 @WWHEWE8 @WWHEWE9 /// @BBHEWE1 @BBHEWE2 @BBHEWE3 @BBHEWE4 @BBHEWE5 @BBHEWE6 @BBHEWE7 @BBHEWE8 @BBHEWE9, family(poisson) link(log) *market exchange desmat: glm Freq HR*WR HE*HR WE*WR @EBBM1 @EBBM2 @EBBM3 @EBWF1 @EBWF2 @EBWF3 @EBWM1 @EBWM2 @EBWM3 @EBBF1 @EBBF2 @EBBF3 /// @WWHEWE1 @WWHEWE2 @WWHEWE3 @WWHEWE4 @WWHEWE5 @WWHEWE6 @WWHEWE7 @WWHEWE8 @WWHEWE9 /// @BBHEWE1 @BBHEWE2 @BBHEWE3 @BBHEWE4 @BBHEWE5 @BBHEWE6 @BBHEWE7 @BBHEWE8 @BBHEWE9, family(poisson) link(log) *both desmat: glm Freq HR*WR HE*HR WE*WR @SEBMWFUp @SEBMWFDown @SEWMBFUp @SEWMBFDown /// @EBBM1 @EBBM2 @EBBM3 @EBWF1 @EBWF2 @EBWF3 @EBWM1 @EBWM2 @EBWM3 @EBBF1 @EBBF2 @EBBF3 /// @WWHEWE1 @WWHEWE2 @WWHEWE3 @WWHEWE4 @WWHEWE5 @WWHEWE6 @WWHEWE7 @WWHEWE8 @WWHEWE9 /// @BBHEWE1 @BBHEWE2 @BBHEWE3 @BBHEWE4 @BBHEWE5 @BBHEWE6 @BBHEWE7 @BBHEWE8 @BBHEWE9, family(poisson) link(log)